Related papers: Generalized Directed Loop Method for Quantum Monte…
We propose a new framework to design and analyze accelerated methods that solve general monotone equation (ME) problems $F(x)=0$. Traditional approaches include generalized steepest descent methods and inexact Newton-type methods. If $F$ is…
Quantum-enhanced Markov chain Monte Carlo, an algorithm in which configurations are proposed through a measured quantum quench and accepted or rejected by a classical algorithm, has been proposed as a possible method for robust quantum…
We explain in detail how to estimate mean values and assess statistical errors for arbitrary functions of elementary observables in Monte Carlo simulations. The method is to estimate and sum the relevant autocorrelation functions, which is…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
Monte Carlo methods have become increasingly relevant for control of non-differentiable systems, approximate dynamics models and learning from data. These methods scale to high-dimensional spaces and are effective at the non-convex…
Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…
Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal…
A treatment of direct simulation Monte Carlo method (DSMC) as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of…
Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the…
The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, molecules, solids and a variety of model systems. The…
Despite their exceptional flexibility and popularity, the Monte Carlo methods often suffer from slow mixing times for challenging statistical physics problems. We present a general strategy to overcome this difficulty by adopting ideas and…
Quantum computing was so far mainly concerned with discrete problems. Recently, E. Novak and the author studied quantum algorithms for high dimensional integration and dealt with the question, which advantages quantum computing can bring…
New hybrid Molecular Dynamics-Monte Carlo methods are proposed to increase the efficiency of constant-pressure simulations. Two variations of the isobaric Molecular Dynamics component of the algorithms are considered. In the first, we use…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
We describe a Monte Carlo simulation study of the magnetic phase diagram of diluted magnetic semiconductors doped with shallow impurities in the low concentration regime. We show that because of a wide distribution of interaction strengths,…
The behavior of a Lattice Monte Carlo algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…